ارزیابی احتمالاتی منحنی های شکنندگی لرزه ای برای سکوی ثابت فلزی با در نظر گرفتن ناپایداری دینامیکی Statistical assessment of seismic fragility curves for steel jacket platforms considering global dynamic instability

Earthquake is one of the most destructive natural disasters which may make drastic damages to the existing structures. Different random nature of earthquake such as occurrence time and location or seismic wave propagation makes it quite complicated for the engineers to anticipate the exact seismic behaviour of the structures. However, after the 1994 Northridge and the 1995 Kobe earthquakes, significant progress was made in earthquake engineering by Federal Management Agency (FEMA) and SAC (joint venture of Structural Engineers Association of California (SEA), Applied Technology Council (ATC), Consortium of Universities for Research in Earthquake Engineering (CUREE)) projects. This highly efficient project has been proposed in FEMA-350/351 guidelines (SAC/ FEMA-2000a, 2000b). The analytical framework of seismic reliability evaluation has been widely expanded by Jalayer and Cornell (Cornell et al. 2002; Jalayer 2003). They derived closed form expressions for the probability of exceeding a limit state considering both aleatoric and epistemic uncertainties in structural and seismic Analyses. This framework became more simplified in a Demand and Capacity Factored Design (DCFD) format (Cornell et al. 2002; Jalayer 2003) which is quite similar to the familiar Load and Resistance Factor Design (LRFD) format (AISC 2003). This format makes it possible to calculate the seismic reliability of the structure at each selected confidence level. In this process, one of the most fundamental assumptions introduced by Shome (1999) is that the maximum interstory drift ratio (MIDR) distributes lognormally at each level of spectral acceleration. It could be easily proven that for a perfectly lognormal random variable (a lognormal population with infinite sample size), the mean of the logarithm of that variable is equal to the logarithm of the median of the same variable (Benjamin and Cornell 1970; Soong 2004). As a result, MIDR demand distributes lognormally around its median at each level of spectral acceleration (Sa) (Shome 1999). However, in a lognormal sample with a finite sample size, the logarithm of the sample median is not exactly equal to the mean of the logarithm of the same sample, and consequently, the mentioned assumption might have some approximations. On the contrary, for any arbitrary random variable the sample geometric mean exactly equals the mean of the logarithm of that sample (Shih and Binkowitz 1967). In this respect, Abyani et al. (2017) compared the analytical framework of seismic reliability evaluation of steel moment frames based on the sample median and the sample geometric mean as the index of central tendency. The results of their study illustrated that the sample geometric mean could lead to more accurate results. From another perspective, in the last two decades, a lot of effort has been made to evaluate and improve the performancebased assessments of the jacket type offshore platforms (JTOPs) (Hasan et al. 2010; Jahanmard et al. 2015; Elsayed et al. 2016). In 1996, Det Norske Veritas (DNV 1996) published a guideline report for the offshore structural reliability which comprised experience and knowledge on the application of probabilistic methods to structural design and provided advice on probabilistic modelling and structural reliability analysis of jacket structures. In another study by Jahanmard et al. (2015), wave endurance time (WET) was addressed as an applicable method for performance-based evaluation of fixed offshore platforms under extreme waves. In this research, artificial wave records called wave functions were designed so that their excitations gradually increase with time. Consequently, the main advantage of this approach was that it could assess the structural performance under various wave load conditions through a single time-history analysis. Elsayed et al. (2016) presented a new method for reliability assessment of a fixed offshore jacket platform against earthquake collapse. They computed the probability of platform collapse under seismic loading using a finite element reliability code. The first and second order reliability methods were used to calculate the safety indices, which could be compared with the target safety levels in offshore platform design codes. Additionally, uncertainty modelling with the nonlinear dynamic analysis of JTOPs was discussed for how to account for the different uncertainties in the reliability assessments. Since jacket platforms may have inelastic behaviour during strong ground motions, it is necessary to use advanced structural analysis methods such as incremental dynamic analysis (IDA) (Vamvatsikos and Cornell 2002). Asgarian and Ajamy (2010) studied the seismic performance of the JTOPs, employing IDA for the structural analysis. They used the story drift as the engineering demand parameter (EDP) and first mode-spectral acceleration as the intensity measure (IM). Golafshani et al. (2011) proposed the method of probabilistic incremental wave analysis (PIWA) to evaluate the performance of JTOPs subjecting to sever wave loadings. In this approach, both static and dynamic wave analyses were implemented to estimate the distribution of wave height intensities. Also, an efficient combination of Latin hypercube sampling (LHS) (McKay et al. 1979) and simulated annealing (SA) technique (Vorechovsky and Novak 2009) was employed to reduce the amount of computational expenses. Further, Ajamy et al. (2014) introduced a comprehensive interaction IDA method to incorporate different sources of uncertainties associated with seismic load, modelling parameters and soil properties in the stochastic seismic analysis of JTOPs. In order to propagate these uncertainties, they used the same combination of LHS and SA technique to model the correlation of the uncertain parameters such as yield strength, elasticity modulus, shear wave velocity, shear modulus reduction and damping ratio. In another study, El-Din and Kim (2014) developed a simple methodology for seismic life cycle cost (LCC) estimation of steel jacket platforms. They utilised equivalent single degree of freedom system instead of the main structure, and eliminated the full IDA and fragility analysis. Instead, approximate fragility curves and localised IDA curves were used as well as a probabilistic simple closed-form solution for loss estimation. In all these studies (Asgarian and Ajamy 2010; Golafshani et al. 2011; Ajamy et al. 2014; El-Din and Kim 2014), it was assumed that the structural demand conditional on a seismic intensity or a wave height level follows a lognormal distribution around its sample median. However, this paper aims to investigate the validity of lognormal hypothesis for the structural demand of JTOP. In this regard, Anderson–Darling (AD) goodness of fit test (Anderson and Darling 1954) has been used to check whether the lognormal distribution is suitable for the structural demand of fixed offshore platforms or not. Furthermore, it is intended to compare the accuracy of seismic fragility curves based on both the sample median and the sample geometric mean as the statistical index of lognormal central tendency, in two regions: (1) where no records has reached the global dynamic instability and (2) at higher intensity levels where the records consecutively reach their collapse capacities.